Related papers: Half precision wave simulation
It is imperative that useful quantum computers be very difficult to simulate classically; otherwise classical computers could be used for the applications envisioned for the quantum ones. Perfect quantum computers are unarguably…
Randomized smoothing is sound when using infinite precision. However, we show that randomized smoothing is no longer sound for limited floating-point precision. We present a simple example where randomized smoothing certifies a radius of…
In recent years, due to a higher demand for portable devices, which provide restricted amounts of processing capacity and battery power, the need for energy and time efficient hard- and software solutions has increased. Preliminary…
Floating point arithmetic allows us to use a finite machine, the digital computer, to reach conclusions about models based on continuous mathematics. In this article we work in the other direction, that is, we present examples in which…
We mechanize the fundamental properties of a rounding error model for floating-point arithmetic based on relative precision, a measure of error proposed as a substitute for relative error in rounding error analysis. A key property of…
In many particle physics experiments the data processing is based on the analysis of the digitized waveforms provided by the detector. While the waveform amplitude is usually correlated to the event energy, the shape may carry useful…
Efforts to reduce the numerical precision of computations in deep learning training have yielded systems that aggressively quantize weights and activations, yet employ wide high-precision accumulators for partial sums in inner-product…
As computer simulations continue to grow in size and complexity, they present a particularly challenging class of big data problems. Many application areas are moving toward exascale computing systems, systems that perform $10^{18}$ FLOPS…
Efficient number representation is essential for federated learning, natural language processing, and network measurement solutions. Due to timing, area, and power constraints, such applications use narrow bit-width (e.g., 8-bit) number…
The massive computational costs associated with large language model (LLM) pretraining have spurred great interest in reduced-precision floating-point representations to accelerate the process. As a result, the BrainFloat16 (BF16) precision…
High-throughput QR decomposition is a key operation in many advanced signal processing and communication applications. For some of these applications, using floating-point computation is becoming almost compulsory. However, there are scarce…
Support for arithmetic in multiple precisions and number formats is becoming increasingly common in emerging high-performance architectures. From a computational scientist's perspective, our goal is to determine how and where we can safely…
The number of IoT devices is expected to continue its dramatic growth in the coming years and, with it, a growth in the amount of data to be transmitted, processed and stored. Compression techniques that support analytics directly on the…
In basic computational physics classes, students often raise the question of how to compute a number that exceeds the numerical limit of the machine. While technique of avoiding overflow/underflow has practical application in the electrical…
Due to the limited number of bits in floating-point or fixed-point arithmetic, rounding is a necessary step in many computations. Although rounding methods can be tailored for different applications, round-off errors are generally…
We describe algorithms and data structures to extend a neural network library with automatic precision estimation for floating point computations. We also discuss conditions to make estimations exact and preserve high computation…
The logarithmic number system (LNS) is arguably not broadly used due to exponential circuit overheads for summation tables relative to arithmetic precision. Methods to reduce this overhead have been proposed, yet still yield designs with…
The design of embedded control systems is mainly done with model-based tools such as Matlab/Simulink. Numerical simulation is the central technique of development and verification of such tools. Floating-point arithmetic, that is well-known…
We describe an approximate rational arithmetic with round-off errors (both absolute and relative) controlled by the user. The rounding procedure is based on the continued fraction expansion of real numbers. Results of computer experiments…
The traditional approach to fault tolerant computing involves replicating computation units and applying a majority vote operation on individual result bits. This approach, however, has several limitations; the most severe is the resource…